Does summing up word vectors destroy their meaning?
Summing up a sequence of word vector maybe used in practice sometimes. However, the operation of addition is non-reversible, meaning that once you sum up a few numbers, you cannot get the original numbers back. However summing up a sequence of word vectors may work depending on your task. You should also normalize the values, or just use average value.

For details: https://towardsdatascience.com/document-embedding-techniques-fed3e7a6a25d#ecd3

To feed data with different lengths, you can also try padding and trimming it. Set a constant L for length of paragraph and trim/pad all list of word vectors to this length. Padding adds 0 vectors to the begining of the list and trimming trims the first part of a text until it is equal to L. Even in LSTM networks padding and trimming is still used as even though you can feed as long of a text to a LSTM as you want, you still have to process the word vectors in batches, which requires them to be the same length.

Example code in python on padding/trimming vector:

def pad_trim(list_vec, L):
    //list vec: {vec1,vec2,vec3......}
    //Assuming vecN have a size of 200
    return list_vec[-L:0] if len(list_vec) &gt; L else [[0] * 200] * (L-len(list_vec)) + list_vec


However in inference, you can ignore maximum length if you used a RNN based method, although as the network has not been trained on lengths more than L, it may perform better or worse.

Generally speaking, you should go for concatenating if possible, so you can keep all information in the sentence. However both may work just fine depending on your task. 

For RNN based and CNN based model example, you should check this out:
https://medium.com/jatana/report-on-text-classification-using-cnn-rnn-han-f0e887214d5f